It’s not a conspiracy if it is true!
It means a coordination by 2 or more persons to engage in an enterprise (often underhanded, often criminal) together (often to deceive).
http://dictionary.reference.com/browse/conspiracy
con·spir·a·cy –noun,plural-cies.
1.the act of conspiring.
2.an evil, unlawful, treacherous, or surreptitious plan formulated in secret by two or more persons; plot.
3.a combination of persons for a secret, unlawful, or evil purpose: He joined the conspiracy to overthrow the government.
4.Law. an agreement by two or more persons to commit a crime, fraud, or other wrongful act.
5.any concurrence in action; combination in bringing about a given result.
Dictionary.com Unabridged Based on the Random House Dictionary, © Random House, Inc. 2010.